Is 1 = 0.9999......

[RossGr]

turn it around, Add you number to .999... you will find that for any n you are greater then 1.

also keep in mind that we are NOT talking about the sum n=1 to N as N -> infinity we Have the sum n = 1 to infinity to deal with there is NO limiting process involved, you cannot specify N as N=infinity. so for your number you must evaluate 10^ (-inifinty) this is zero.

 

[Mday]

i love how ppl who dont know what is going on try to answer the problem at hand.
this has been a blind post btw. not necessarily a response to ppl who posted directly above me.

 

[josphII]

Originally posted by: SilentRunning

Originally posted by: silverpig

Originally posted by: GroundZero
depends on how you look at it.
0.999... is as close to 1 as you can get mathmatically, but it will still be short of 1 by the smallest amount imaginable.

What is this amount?

For any n:

1 = (Sum(i = 1..n)[9/10^i]) + 10^(-n)

so for n=3:

1 = (0.9+0.09+.0.009) + 10^ (-3)
1 = 0.999 + 0.001
1 = 1

Let n --> inf

you cant do that. you cant just arbitrarily take the limit of something. your initial expression holds true for n equals infinity

1 = (Sum(i = 1..inf)[9/10^i]) + 10^(-n) (as n--> inf)

But

0.999... = Sum(i = 1..inf)[9/10^i]

Therefore

1-0.999... = [(Sum(i = 1..inf)[9/10^i]) + 10^(-n)] -[Sum(i = 1..inf)[9/10^i]] (as n --> inf)
1-0.999... = [(Sum(i = 1..inf)[9/10^i]) - [Sum(i = 1..inf)[9/10^i]] + 10^(-n) (as n --> inf)
1-0.999... = 10^(-n) (as n --> inf)



Edit fixed this line 1 = (0.9+0.09+.0.009) + 10^ (-3)

 

[Bachopoet]

_
lim(1)=.9999

...consider the infinite.

 

[silverpig]

Originally posted by: SilentRunning

Originally posted by: RossGr

1-0.999... = 10^(-n) (as n --> inf)

Ok, now that you have taken this far you need to complete it.

1-0.999... = 10^(-n) (as n --> inf)= 0

Therefore 1= .999....

Nope it doesn't = 0, it tends toward zero

If you examine the equations the difference is equal to the remainder that one must ignore when dividing 1 by itself to result in the answer 0.999...


Do you understand that infinite is the opposite of finite? As n --> infinity you will never reach it, it will never have a finite value. That is why we have limits.

It tends towards zero as n tends to infinity, but the description of 0.999... is a decimal point followed by an infinite string of 9s, not a point followed by n nines as n tends to infinity.

 

[SilentRunning]

One day a caveman and his significant other stumble upon a plant. They take it home and eat it. However, they save the seeds and plant them. The plants grow and prosper. They calculate that each day they each will be able to eat 9 plants for as long as they live. This in itself is amazing because math doesn?t exist.

So the gardens are planted. They each have their own garden. The caveman accidentally plants one more seed than his wife. When the first plants are fully grow, the caveman fearing anger from his mate hides the extra plant under his stone pillow. Comparing the first day?s crop both only have 9 plants.

For each successive day they each have 9 plants ready to be harvested. Meanwhile the plant hiding under the caveman?s pillow decomposes and begins to stink. His mate just thinks it?s his B.O. Over time the plant decomposes into it separate atomic parts. These atoms recombine with other atoms to form new compounds.

Before her death the caveman?s mate confronts him and says, ?I know you had more plants than me, I saw you stick the extra one under the pillow the first day.?

The caveman says no you are wrong we had exactly the same number of plants. He lifts stone pillow and shows her that there is no plant under the pillow.


So either you think like the caveman or his significant other.

 

[RossGr]

Clearly, like you your cavemen have no concept of infinity.

I,2 , 3 ...many, isn't that how you count?

Your analogy has nothing to do with the situation being discussed. You simply cannot use a finite set to prove anything in this argument.

When we write .99.... it is not like walking along the 9s setting a new nine down with each step, instead you have 9s already in place, to the horizon and beyond (or to quote Buzzlightyear "To Infinity, And Beyond!).

For a correct handling of your "proof" Read this. This starts with a geometric series proof, which is completly valid, but not from basics. Following the Geometric Series proof is a proof form basics which does NOT take any limits and handles the infinty correctly. Please consider it carefully and remember that in real analysis equality is defined as x=y iff Abs(x-y)< d for any d>0 if this fact can be established you have x=y.

 

[DoNotDisturb]

how did you create that?

 

[GiLtY]

Well if it's a number with infinite 9's I'd agree it is equal to 1, because it makes sense if you think between fraction and integer (1/3 = .33333..........). But if you cut the decimals off at some point it will not be one..

 

[MadRat]

RossGR-

I see the reason you have a problem with infinity being definitive. All your link did was try to say 1-.999...=0, which is not true.

It did not prove the point except that whatever sliver is between .999... and 1 the result of the math is incomprehensible.

 

[MadRat]

Originally posted by: Beast1284
The best argument I found in the thread was that they must be equal because there is no number between 0.99..... and 1.

The problem is that .999... has no definitive form from which to calculate 1-.999...., meaning there is no answer to the comparison.

However, their argument that it should equal "1" is pointless, because there is a limit placed on the value that prevents it from reaching the value of "1". Infinity in this case is striated to only an expansion of the decimal, and what happens to the decimal has no effect on the value of the "0" that is assumed in front of the 9's. It becomes trapped below "1" because if its value at the 10^-1 decimal place.

 

[silverpig]

Originally posted by: MadRat
RossGR-

I see the reason you have a problem with infinity being definitive. All your link did was try to say 1-.999...=0, which is not true.

It did not prove the point except that whatever sliver is between .999... and 1 the result of the math is incomprehensible.

PLEASE, explicilty define this so called sliver.

 

[silverpig]

Originally posted by: MadRat

Originally posted by: Beast1284
The best argument I found in the thread was that they must be equal because there is no number between 0.99..... and 1.

The problem is that .999... has no definitive form from which to calculate 1-.999...., meaning there is no answer to the comparison.

However, their argument that it should equal "1" is pointless, because there is a limit placed on the value that prevents it from reaching the value of "1". Infinity in this case is striated to only an expansion of the decimal, and what happens to the decimal has no effect on the value of the "0" that is assumed in front of the 9's. It becomes trapped below "1" because if its value at the 10^-1 decimal place.

0.999... = 1 and either one of these is the definitive form.

The limit prevents it from becoming GREATER than 1...

 

[MadRat]

Originally posted by: silverpig

Originally posted by: MadRat
RossGR-

I see the reason you have a problem with infinity being definitive. All your link did was try to say 1-.999...=0, which is not true.

It did not prove the point except that whatever sliver is between .999... and 1 the result of the math is incomprehensible.

PLEASE, explicilty define this so called sliver.

Some things have no value that can be defined. Can you define God?

 

[RossGr]

Matrat are you tottal blind? Or can you simply not read?
My final result DOES NOT RELY ON .99... + or - any thing! It shows that .999.... is standwitched between 1 and ANY NUMBER added to or subtracted from 1. There is ONLY 1 number for which this can be possibly true, 1. I have shown that .999..... satisfies this conditon.

I have shown that ANY number added to .999.... results in a number bigger then 1. I did not specify anything other then the fact that it is greater, are you arguing with that?

 

[SilentRunning]

Originally posted by: RossGr
Clearly, like you your cavemen have no concept of infinity.

I,2 , 3 ...many, isn't that how you count?

Your analogy has nothing to do with the situation being discussed. You simply cannot use a finite set to prove anything in this argument.

When we write .99.... it is not like walking along the 9s setting a new nine down with each step, instead you have 9s already in place, to the horizon and beyond (or to quote Buzzlightyear "To Infinity, And Beyond!).

For a correct handling of your "proof" Read this. This starts with a geometric series proof, which is completly valid, but not from basics. Following the Geometric Series proof is a proof form basics which does NOT take any limits and handles the infinty correctly. Please consider it carefully and remember that in real analysis equality is defined as x=y iff Abs(x-y)< d for any d>0 if this fact can be established you have x=y.

All I have to say is whoever wrote the second proof in the link must be totally oblivious to all logic. The are attempting to find the sum of something that isn't defined as a sum. They just don't understand infinity. Because a value approaches infinity does not mean that it is a sum to infinity.

 

[RossGr]

All I have to say is whoever wrote the second proof in the link must be totally oblivious to all logic. The are attempting to find the sum of something that isn't defined as a sum. They just don't understand infinity. Because a value approaches infinity does not mean that it is a sum to infinity.

YOu are not making any sense what so ever.

you disagree that the the sum of .1^n for any number to infinity is greater then zero?

That is the only use I made of infinty.

You really need to take a math course beyond basic calculus.

 

[SilentRunning]

Originally posted by: RossGr

All I have to say is whoever wrote the second proof in the link must be totally oblivious to all logic. The are attempting to find the sum of something that isn't defined as a sum. They just don't understand infinity. Because a value approaches infinity does not mean that it is a sum to infinity.

YOu are not making any sense what so ever.

you disagree that the the sum of .1^n for any number to infinity is greater then zero?

That is the only use I made of infinty.

You really need to take a math course beyond basic calculus.

And what does that have to do with the question at hand. We aren't talking about the sum of 0.1^n.

And what makes you think I have only had basic calculus?

 

[SilentRunning]

RossGR,

Does (ab+c) for the values a = 2, b = 5, c= 9, equal

a. 19
b. 28
c. none of the above

Explain your reasoning.

 

[spidey07]

LOL.

Its just funny to read the thread and responses.

"Here are many proofs and manipulations that show how .999 equal 1. Here are many more showing how and why they are not different"

Response - "well that's simply not the case...you see in my universe and philsophy the two are not equal. Although I have no reasoning or any sound basis to show what I believe in my universe, it is still my universe so your rules don't apply."

 

[spidey07]

Explain your reasoning

two groups of five apples when counted is 10 apples
Another pile containg 9 apples is added to the pile
count the apples using the real number system = 19 apples.

 

[RossGr]

Originally posted by: SilentRunning
RossGR,

Does (ab+c) for the values a = 2, b = 5, c= 9, equal

a. 19
b. 28
c. none of the above

Explain your reasoning.

What has this to do with the price of eggs in China?

I say you have only had a basic course in calculus because that is the level of misunderstanding that you are displaying.

we are not talking about the behavior of .1^n as n-> infinity, we are talking about the equality of 1 and .99....

My proof is valid.

BTW: it was written in Word '97 with Equation editor 3.0 then printed to PDF useing adware from here

 

[SilentRunning]

I was trying to see if you understand what mathematical conventions are. Do you think mathematical conventions have any bearing on math or do you just plain ignore them.

 

[MadRat]

Originally posted by: RossGr
Matrat are you tottal blind? Or can you simply not read?
My final result DOES NOT RELY ON .99... + or - any thing! It shows that .999.... is standwitched between 1 and ANY NUMBER added to or subtracted from 1. There is ONLY 1 number for which this can be possibly true, 1. I have shown that .999..... satisfies this conditon.

I have shown that ANY number added to .999.... results in a number bigger then 1. I did not specify anything other then the fact that it is greater, are you arguing with that?

But .999... doesn't exist in the same respect as 1 so its impossible to find the difference. If they were comparable then you could add the difference of 1 and .999... back to .999... to make 1 again. However, since you cannot even agree that ".999..." does end in a 9 at the infinite spot then how can you even begin to understand your fallacy?

When you subtract 99 from 100 there is a remainder of 1. We subtract from the righthand column first, taking a 9 from a 0. This isn't possible so we steal something from the 10^1 digit to the left of the rightermost "0". In this case its another 0! So we take the "1" from the 10^2 column and turn it into a zero, the 10^1 value now becomes a "9" and the 10^0 value becomes a "10". Nine from 10 results in a remainder of 1! So 100-99=1.

We can also do this with 1-.999... to deduce that the answer is a remainder of 1 at the point of the infinite (10^-n, n=infinity) decimal place. There is no universally recognized symbol for this value, nor can mathematically trained individuals like yourself even relate to the simplicity of its definition. Just as .999... would be the point theoretically closest to 1 without reaching it, .000...r1 would be the point closest to null without reaching zero. Somewhere in the last two decades the translation of infinity turned into a meaning ripe of counter-intuition. Just because it sounds good to say ".999... should be 1" doesn't mean it is remotely true.

 

[spidey07]

Madrat,

You do realize that the concept of infinity allows us to do things like build bridges, space shuttles, use nuclear power safely, etc?

Without it math (specifically calculus) doesn't work in the natural world. With it and by using infinity we can understand nature and the world.

Your explanations simply do not follow the natural world, hence you must be using your "own universe"